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On a Conjecture of Alzer, Berg, and Koumandos

Author

Listed:
  • Ladislav Matejíčka

    (Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in Trenčín, I. Krasku 491/30, 02001 Púchov, Slovakia)

Abstract

In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function.

Suggested Citation

  • Ladislav Matejíčka, 2020. "On a Conjecture of Alzer, Berg, and Koumandos," Mathematics, MDPI, vol. 8(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1031-:d:375279
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